Question

What is the midpoint of this line segment?
E(-6,1) F(2,-5)

(2,2)
(-2,-2)
(1/2, -1/2)
(-5/2, -3/2)

Answer 1

To find the midpoint of a line segment defined by two points \( E(x_1, y_1) \) and \( F(x_2, y_2) \), you can use the midpoint formula:

\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

For the points \( E(-6, 1) \) and \( F(2, -5) \):

- \( x_1 = -6 \)
- \( y_1 = 1 \)
- \( x_2 = 2 \)
- \( y_2 = -5 \)

Plugging these values into the midpoint formula:

\[
M = \left( \frac{-6 + 2}{2}, \frac{1 + (-5)}{2} \right)
\]
\[
M = \left( \frac{-4}{2}, \frac{-4}{2} \right)
\]
\[
M = (-2, -2)
\]

So, the midpoint of the line segment \( EF \) is \( (-2, -2) \).

Among the provided options, the correct answer is \( (-2, -2) \).